Range of row n of the Circular Pascal array of order 4. - Shaun V. Ault, May 30 2014

a(n) is the number of permutations of length n avoiding both 213 and 312 in the classical sense which are breadth-first search reading words of increasing unary-binary trees. For more details, see the entry for permutations avoiding 231 at A245898. - Manda Riehl, Aug 05 2014

Also, the decimal representation of the diagonal from the origin to the corner (and from the corner to the origin except for the initial term) of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 190", based on the 5-celled von Neumann neighborhood when initialized with a single black (ON) cell at stage zero. - Robert Price, May 10 2017

a(n + 1) + n - 1, n > 0, is the number of maximal subsemigroups of the monoid of partial order-preserving or -reversing mappings on a set with n elements. See the East et al. link. - James Mitchell and Wilf A. Wilson, Jul 21 2017

Number of symmetric stairs with n cells. A stair is a snake polyomino allowing only two directions for adjacent cells: east and north. See A005418. - Christian Barrientos, May 11 2018

For n >= 4, a(n) is the exponent of the group of the Gaussian integers in a reduced system modulo (1+i)^(n+2). See A302254. - Jianing Song, Jun 27 2018

a(n) is the number of length-(n+1) binary sequences, denoted <s(1),...,s(n+1)>, with s(1)=1 and with s(i+1)=s(i) for odd i. - Dennis P. Walsh, Sep 06 2018